To find \(m + 2r\), we first need to calculate the mean (average) height and the range of heights.

Mean Height (\(m\)):

\[

m = \frac{1.35 + 1.25 + 1.35 + 1.40 + 1.35 + 1.50 + 1.35 + 1.50 + 1.20}{9}

\]

Calculate the sum of the heights:

\[

\text{Sum} = 1.35 + 1.25 + 1.35 + 1.40 + 1.35 + 1.50 + 1.35 + 1.50 + 1.20 = 12.25

\]

Divide by the number of heights (9):

\[

m = \frac{12.25}{9} = 1.3611 \approx 1.36

\]

Range of Heights (\(r\)):

The range of heights is the difference between the maximum and minimum heights:

\[

r = \text{Maximum Height} - \text{Minimum Height}

\]

Sort the heights in ascending order:

1.20, 1.25, 1.35, 1.35, 1.35, 1.40, 1.50, 1.50, 1.35

Maximum Height = 1.50

Minimum Height = 1.20

\[

r = 1.50 - 1.20 = 0.30

\]

Now, compute \(m + 2r\):

\[

m + 2r = 1.36 + 2 \times 0.30 = 1.36 + 0.60 = 1.96

\]